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Plasma Science: From Fundamental Research to Technological Applications 2 Nonneutral Plasmas INTRODUCTION AND BACKGROUND A nonneutral plasma is a many-body collection of charged particles in which there is not overall charge neutrality. Such systems are characterized by self-electric fields and, in high-current configurations, self-generated magnetic fields. Single-component plasmas are an important class of nonneutral plasmas, the most common examples of which are pure electron and pure ion plasmas. For single-component plasmas in cylindrical geometry, there exists a stringent confinement theorem. The practical consequence of this theorem is that, in contrast to electrically neutral plasmas, a magnetized single-component plasma can be confined easily for very long times (e.g., hours). Therefore, thermal equilibrium and controlled departures from equilibrium can be achieved readily. Nonneutral plasmas exhibit a broad range of collective plasma behavior, such as plasma waves, instabilities, and Debye shielding. Moreover, the rotation and self-generated fields in these plasmas can have a significant effect on plasma properties and stability behavior. In addition to their importance in understanding fundamental aspects of the behavior of many-body charged-particle systems, there are many practical applications of nonneutral plasmas. Examples discussed elsewhere in this report include the generation of coherent radiation by intense charged-particle beams, the development of advanced accelerator concepts, and the stability of electron and ion flow in high-voltage diodes. Other applications include particle-beam fusion, and the stability and propagation of intense charged-particle beams through background plasma or through the atmosphere. This section focuses
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Plasma Science: From Fundamental Research to Technological Applications specifically on single-component plasmas, with emphasis on pure electron and pure ion plasmas. Research and development in this area is likely to have a significant impact on a wide range of important applications, such as new generations of precision clocks; chemical analysis by improved methods of mass spectrometry; and the accumulation, storage, and transportation of antimatter. Early research on nonneutral plasmas predated by many decades common usage of the term "plasma." For example, efforts to investigate the equilibrium and stability properties of nonneutral electron flow began with Child (1911), and continued with the work of Langmuir (1923), Llewellyn (1941) and Brillouin (1945), and work on beam-type microwave devices in the 1940s and 1950s. During the past 20 years, interest in the physics of single-component plasmas has grown substantially in such diverse areas as the equilibrium, stability, and transport properties of these plasmas; phase transitions in two- and three-dimensional plasmas; astrophysical studies of large-scale nonneutral plasma regions in the magnetospheres of neutron stars; and the development of positron and antiproton ion sources. In the case of trapped-ion plasmas, an important synergism has developed between atomic physicists and plasma physicists. Atomic physicists have developed methods to confine and study small collections of ions with great precision. With the addition of more particles, issues of collective oscillations and confinement properties of spatially extended, three-dimensional plasmas become relevant and raise a number of important questions. Study of these questions has illuminated fundamental issues in plasma physics. It has resulted in enhanced capabilities in the creation and control of pure ion plasmas for precision measurements of fundamental constants and for applications such as atomic clocks. A significant fraction of nonneutral plasma research is closely tied to important technological applications. In contrast to the general development of fundamental plasma experiments that has been hindered significantly in the past two decades due to lack of support, experimental progress in nonneutral plasma research has been excellent, which has stimulated much progress in the theory of nonneutral plasmas. It is the conclusion of the panel that the relative success of research on nonneutral plasmas was due to a strong and dedicated program of support in this area by the Office of Naval Research, with complementary support from the National Science Foundation and the Department of Energy. The panel concludes that this mode of support for nonneutral plasma research should be considered a model for the support of fundamental plasma experiments in the broader area of neutral plasma research. RECENT ADVANCES IN NONNEUTRAL PLASMAS The following summarizes significant advances in the physics of nonneutral plasmas during the past decade.
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Plasma Science: From Fundamental Research to Technological Applications Electron Plasmas Much progress has been made in understanding the basic physics of single-component plasmas, including critical aspects of the stability, confinement, and equilibrium of these plasmas. It was shown theoretically that the conservation of canonical angular momentum implies, in the absence of external torques, that a single-component plasma can be confined indefinitely. Soon afterward, it was demonstrated that the confinement of pure electron plasmas for several minutes to hours is relatively easily achievable in laboratory experiments. The confinement times are sufficiently long that the plasma approaches a state of thermal equilibrium. The existence of these thermal equilibrium states in confined, single-component plasmas distinguishes them from neutral plasmas. A magnetically confined neutral plasma does not remain in a state of spatially isolated, local thermal equilibrium, because collisions between the electrons and ions lead to a diffusive expansion of the plasma across magnetic field lines. In addition, in a neutral plasma there is typically free energy (associated with the relative cross-field flow of electrons and ions) available to drive collective instabilities that produce enhanced transport across the field lines. Such instabilities pose a challenge to the achievement of high-quality confinement in electrically neutral plasmas of interest in fusion. In contrast, a confined, single-component plasma that has come to thermal equilibrium is in a state of minimum free energy and hence is stable. It is also a great advantage theoretically to be able to use thermal equilibrium statistical mechanics to describe the equilibrium state. Theory predicted that, in a strong magnetic field and at low temperature, the relaxation of the particle velocities to a thermal equilibrium distribution would be constrained by an adiabatic invariant, and as a consequence, the relaxation rate would be exponentially small. Subsequent experiments confirmed this prediction, and now there is good agreement between theory and experiment over eight orders of magnitude in effective magnetic field strength and five orders of magnitude in the scaled relaxation rate. The well-controlled nature of these plasmas has also permitted precise studies of nonequilibrium states unachievable in other plasmas. For a sufficiently low-density nonneutral plasma, in the limit that transport along magnetic field lines is rapid compared to transport perpendicular to the field, the plasma is described by similar equations (in an isomorphic sense) to those describing an inviscid classical fluid in two dimensions. Charge-density perturbations in a single-component plasma are analogous to vortices in a fluid, and vortex dynamics is an important subject of long-standing interest in fluid dynamics. Recently, this analogy has begun to be exploited to test models of coherent structures and vortex merger with a precision not possible in classical fluids. For example, since the effective viscosity of a pure electron plasma is less by orders of magnitude than the viscosity of a classical fluid, the trajectories of a pair of vortices
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Plasma Science: From Fundamental Research to Technological Applications can be followed for 104 or 105 orbits before merger occurs. In the case of classical fluids such as water, merger or dissipation typically occurs in a few orbits. Finally, a nonneutral plasma exhibits a wide range of collective waves and instabilities analogous to those observed in an electrically neutral plasma, appropriately modified by self-field effects. These collective waves and instabilities have been documented extensively in theoretical analyses, and algorithms have been developed for calculating the detailed stability behavior or nonneutral plasma over a wide range of system parameters. In addition, a kinetic stability theorem has been developed that determines a sufficient condition for the nonlinear stability of cylindrically symmetric equilibria to arbitrary-amplitude perturbations, including the influence of strong self-field effects. Ion Plasmas Another type of single-component plasma that has been studied extensively is the magnetized, pure ion plasma, confined in a Penning trap, and cooled by laser radiation. In this case, the laser light is used both to cool the ions and to exert a torque on the plasma. This torque has the effect of spinning up the plasma and compressing it. An analytical theory of the collective modes of oscillation in these plasmas has been formulated on the basis of cold fluid theory. This is the first analytical description of the modes of a magnetized, three-dimensional plasma of finite extent with realistic boundary conditions. There is good agreement between theory and the experimental observation of these modes. One result of this increased understanding is that these modes can now be used for the manipulation and confinement of pure ion plasmas. An exact nonlinear theory has been developed for the case of large-amplitude quadrupole modes of oscillation of these plasmas. In ion plasmas that are laser-cooled to cryogenic temperatures, the average kinetic energy per particle can be made small compared to the average interaction potential energy. (These plasmas are often referred to as strongly coupled plasmas.) The resulting ion clouds can form the analogues of dense liquid and solid phases. (See Figure 2.1.) Theoretical and experimental progress has been made recently in understanding the ordering and equilibrium states of these systems. As the temperature is lowered, theory predicts that the ions arrange themselves in concentric spheroidal shells. These shells are the analogues of crystal planes, except that the planes are deformed into spheroids because of the small plasma size. This shell structure has been observed experimentally, with optical imaging techniques, for plasmas up to about 15 shells. Theory predicts that the sample must contain about 60 shells to result in the structure predicted for plasmas of infinite extent (a body-centered-cubic lattice), but this has not yet been tested experimentally. Small numbers of ions have also been confined and cooled in Paul traps,
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Plasma Science: From Fundamental Research to Technological Applications which utilize the ponderomotive force from high-frequency electric fields to confine the ions. At low temperature, Coulomb repulsion between the ions causes the ions to crystallize into simple geometrical configurations (Coulomb clusters) whose shapes can be predicted theoretically. These clusters and ordered one-dimensional chains of ions have now been observed and studied in Paul traps. (See figure 2.1a.) As the number of ions is increased, experiments have observed polymorphic phase transitions to more complex lattice structures: first a zigzag arrangement, then a helical chain, and finally a cylindrical shell structure, similar to the spheroidal shells observed in Penning traps. These phase transitions have also been studied theoretically. Such linear lattice structures also are predicted to occur in chains of ions confined and cooled in a heavy-ion storage ring. In the rest frame of the ions circulating in such a storage ring, the confining forces are nearly the same as those in the linear Paul trap described above. The theoretical density limit for the confinement of a magnetized, single-component plasma occurs when the square of the plasma frequency is one-half the square of the cyclotron frequency (Brillouin, in 1945). This "Brillouin density limit" has been achieved in pure ion plasmas by using laser radiation to exert torques on the plasma and thereby to compress it. In a "cold" one-component plasma column, the radially outward space-charge and centrifugal forces on a fluid element balance the inward magnetic confining force (i.e., the Lorentz force). This places a limit on the maximum plasma density that can be confined for a given value of magnetic field (i.e., the Brillouin density limit). The rotation frequency at the Brillouin limit is such that the Lorentz force on the plasma particles is just canceled by the Coriolis force, and the plasma is effectively unmagnetized when viewed in the rotating frame. Therefore, at the Brillouin limit, it is possible to study in detail a fundamentally new plasma regime in which the confined plasma is effectively "unmagnetized.'' Ion Plasmas in Electron-Beam Ion Traps The electron-beam ion trap configuration, which was invented in the last decade, uses a magnetically compressed electron beam, with energies in the range of several hundred keV, to ionize, trap, and excite highly charged ions of a wide variety of elements for atomic physics measurements. Electron-beam ion trap devices are capable of producing high-resolution x-ray spectra of nearly stationary ions that have been excited by monoenergetic electrons. One can also vary the energy of the electron beam on a time scale fast compared to that for changes in the ionization states of the ions. Thus, the ions can be excited with electrons of one energy and probed with electrons of a different energy. These devices have been able to produce one-electron (i.e., hydrogen-like) ions up to nuclear charge Z = 92. In the last few years many important measurements have been made utilizing electron beam ion trap devices for atomic phys-
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Plasma Science: From Fundamental Research to Technological Applications FIGURE 2.1 Correlated behavior observed when small, single-component ion plasmas are laser cooled to temperatures of a few tens of millikelvin. Such laser-cooled ion plasmas are being used to improve the performance of atomic clocks and frequency standards. (a) A crystallized chain of 15Hg+ ions, confined in an rf trap by the electrode structure shown. (b) Be+ ions confined in a Penning trap, imaged by passing three crossed laser beams through the plasma. The bright fringes are the intersections of the laser beams with the plasma's lattice planes, which take the form of approximately spheroidal shells. The plasma rotates about its symmetry axis (normal to the figure), which obscures the image of individual ions within each shell. (Courtesy of J. Bollinger and D. Wineland, National Institute of Standards and Technology, Boulder, Colo.)
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Plasma Science: From Fundamental Research to Technological Applications ics, including tests of leading theories of atomic structure and crucial tests of extrapolations of previous, lower-Z measurements. Other important experiments include x-ray observations of magnetic octopole decay in atomic spectra; the first use of x-ray polarization to probe the hyperfine interaction in highly charged ions; the first direct measurements of ionization cross sections for highly charged ions; the first measurements of dielectronic recombination cross sections in ions that are important in hot fusion plasmas; the first excitation functions for x-ray lines used in the analysis of high-temperature tokamak and astrophysical plasmas; measurements of line overlaps for x-ray laser design; and measurements of metastable lifetimes in regions of the electromagnetic spectrum inaccessible to other techniques. Confinement of Antimatter Trapping techniques similar to those described above for pure electron plasmas have proved to be an efficient way to accumulate and store antimatter particles such as positrons and antiprotons. Single-component positron plasmas, a few cubic centimeters in volume, with a temperature of 300 K and Debye screening lengths less than 1 mm have now been created in the laboratory by accumulating positrons from a radioactive source. Recently, antiprotons from the low-energy antiproton storage ring at CERN in Geneva have been captured by a similar trapping scheme. The antiprotons were cooled to 4 K by collisions with an electron plasma confined in the same cryogenic trap. These experiments have provided a controlled way to study antimatter interactions with ordinary matter and to study the properties of the antimatter particles themselves. Examples include precision measurements of the mass of the antiproton and positron annihilation phenomena relevant to atomic and molecular physics and to gamma-ray astronomy. RESEARCH OPPORTUNITIES Continued progress is expected in the areas identified above in "Recent Advances in Nonneutral Plasmas." In addition, the following topics, while not comprehensive or mutually exclusive, represent important research opportunities in the physics of nonneutral plasmas.
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Plasma Science: From Fundamental Research to Technological Applications Coherent Structures and Vortex Dynamics The progress made during the past decade in studies of single-component plasmas has created a number of important scientific and technological opportunities. The ability to confine and manipulate pure electron plasmas and to create near-equilibrium states opens up unique opportunities to study transport in plasmas and fluids. The equations that govern two-dimensional flows in these plasmas are identical to the equations that govern two-dimensional flows in inviscid incompressible fluids. Exploiting this analogy, researchers have now conducted successful studies of vortex merger in electron plasmas, and the opportunity now exists to study important phenomena in fluid mechanics, such as the relaxation of two-dimensional turbulence (see Plate 2), the interaction of vortices with turbulence and shear flows, and turbulent transport. Transport Processes On longer time scales, the transport of particles due to like-particle collisions is only partially understood. In principle, this is a more difficult problem than the interaction of two-dimensional vortices because three-dimensional effects may be important, as well as the combined effects of single-particle and collective interactions. These effects are related to fundamental issues in kinetic theory and transport processes in neutral plasmas, but they can be isolated and studied more easily in single-component plasmas because of the unusually long confinement times. Confinement Properties in Nonaxisymmetric Geometries Recently, magnetized, single-component electron plasmas have been created that are not symmetric in the plane perpendicular to the confining magnetic field. (See Figure 2.2.) These plasmas were found to have surprisingly long confinement times. It does not appear that these long-lived, asymmetric states can be explained by the simplest models of good confinement of single-component plasmas with cylindrical symmetry, which indicates that the fundamental principles of single-component plasma confinement are not fully understood. Stochastic Effects In complex magnetic field geometries, the combined influence of the applied field configuration and the self-electric and self-magnetic fields of the nonneutral electron or ion beam can significantly affect individual particle motion and beam dynamics. For example, this can occur in the periodic wiggler field in free-electron lasers or in the periodic quadrupole focusing field in induction accelerators, particularly at sufficiently high beam intensities. Although the
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Plasma Science: From Fundamental Research to Technological Applications FIGURE 2.2 Shown is the cross section of a magnetized pure-electron plasma confined in a Penning trap. These plasmas were found to exhibit unexpectedly long confinement times. This good confinement is consistent with a recently developed theory that argues that such states are stable equilibria. The plasma is distorted into a triangular shape by the application of electrical potentials (indicated in volts) to sections of a cylindrical electrode structure. The calculated equipotential contours (solid lines) illustrate that the plasma edge follows such a contour. Note that the electrons are closer to the negative electrodes, as expected for a state of maximum electrostatic energy, and as predicted by the theory. (Reprinted, by permission, from J. Notte, A.J. Peurrung, J. Fajans, R. Chu, and J.S. Wurtele, Physical Review Letters 69:3056, 1992. Copyright © 1992 by the American Physical Society.) particle dynamics are characterized by well-defined single-particle constants of the motion at low beam intensity, where self-field effects are negligibly small, at higher beam intensity the particle orbits can become chaotic and sensitive to the detailed properties of the beam density and current profiles. We do not have a basic understanding of the influence of stochastic effects on the charge homogenization in periodic focusing quadrupole configurations or on the suppression of coherent free-electron-laser emission at high beam intensity. Strongly Coupled Nonneutral Plasmas Strongly coupled pure ion plasmas present another set of scientific opportunities. The evolution of the spatial ordering to the body-centered-cubic structure
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Plasma Science: From Fundamental Research to Technological Applications that is expected for a large-volume plasma remains to be studied experimentally. Such experiments will test the predictions of recent theories. Furthermore, for modest-sized plasmas, the theoretical prediction of ordering in concentric spheroidal shells is at variance with observations of open cylindrical shells. This significant discrepancy also remains to be reconciled. Although there is now a good understanding of many features of the equilibria of ion plasmas and of the linear dynamics of these plasmas about their equilibria, many important questions remain. For example, the transport coefficients (such as the viscosity and the thermal relaxation time) in strongly correlated, magnetized, nonneutral plasma are not understood theoretically. Experiments can measure many of these coefficients. It is likely that future interplay between theory and experiment in this area will be productive in elucidating these fundamental transport processes. Quantum-Mechanical Effects The tools now exist to create plasmas in correlated spin states and to create quantized plasmas, in which the quantum-mechanical ground state energy is large compared to the thermal energy in a plasma mode. Another important area for future study relates to the properties of nonneutral plasmas at or near the Brillouin density limit. Antimatter The efficient trapping of single-species plasmas has been exploited for the confinement and cooling of both antiprotons and positrons. Further progress in developing efficient techniques for the confinement and manipulation of single-species plasmas will directly benefit studies of antimatter and the interaction of antimatter with ordinary matter. Improvements in the trapping and manipulation of single-component plasmas will lead to the ability to transport antimatter (such as antiprotons) from high-energy accelerators, where they are created, to laboratories throughout the world. Many important scientific questions can be addressed by collections of antimatter particles confined in traps. For example, one can study the physics of electron-positron plasmas. These plasmas are unusual in the sense that both signs of charge can be highly magnetized, and the "electron-ion" mass ratio is unity. Important physics issues include the nature of confinement and transport in these neutral but highly magnetized plasmas and the nature of fluctuations and turbulence in such equal-mass plasmas. The interaction of low-energy positrons with ordinary matter can also be studied with precision in traps, to address questions relevant to atomic and molecular physics and to gamma-ray astronomy. The 511-keV gamma-ray annihilation line is the strongest astrophysical source of gamma-ray line radiation. Trapped antiprotons will be of use for fundamental
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Plasma Science: From Fundamental Research to Technological Applications physics measurements on the antiprotons themselves. Moreover, addition of a cold positron plasma to the trapped antiprotons is thought to be the simplest way to produce cold antihydrogen, which would be the first creation of neutral anti-matter in the laboratory. OPPORTUNITIES FOR ADVANCES IN TECHNOLOGY Precision Clocks A wide range of technological opportunities is likely to result from research on laser-cooled ion plasmas. Spectroscopic interrogation of ions in traps is one of a few possible techniques for developing a new generation of precision clocks. Improvements in clocks using pure ion plasmas hinge on understanding the microscopic distribution function of the ions or, equivalently, on a more quantitative theoretical understanding of strongly coupled plasmas. Improved precision clocks would lead to advances in such diverse areas as navigation and tests of general relativity. Precision Mass Spectrometry One of the most important techniques for studying the masses of chemical species is ion cyclotron resonance, where the cyclotron motion of a confined cloud of ions is excited and detected. A large signal-to-noise ratio requires a large number of ions, but in this case precise interpretation of the cyclotron resonance signal hinges on a detailed understanding of the collective modes of oscillation of these multispecies ion plasmas. Scientific issues in this area have only recently begun to be addressed, starting with studies of the cyclotron modes of a single-component electron and ion plasmas, and precision studies of cyclotron resonance for one or a few ions. It is likely that much progress can be made in this area during the next decade. Ion Sources with Enhanced Brightness Laser cooling of 1-MeV ions in storage rings has recently been achieved. The development of methods for cooling these single-component plasmas and understanding their behavior can lead to brighter ion beams and hence to enhanced accelerator performance. It is possible that the "sympathetic cooling" of ions confined in a trap with positrons will lead to brighter sources of positrons for advanced accelerators. The successful achievement of cryogenic plasmas opens up the possibility of preparing spin-polarized plasmas. In principle, these plasmas could provide bright sources of polarized particles for use in particle accelerators.
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Plasma Science: From Fundamental Research to Technological Applications Electron-Beam Ion Traps Studies of electron-beam ion traps as plasma devices are in their infancy, and progress in this area could lead to performance enhancements by several orders of magnitude. This would enable new kinds of experiments in atomic, nuclear, and surface physics. An enhanced ion source based on the electron-beam ion trap is expected to be useful for surface modification and nanotechnology. In most cases, plasma physics issues are the key to these developments. For example, a thousandfold increase in the x-ray emission rate from an electron-beam ion trap might be achieved by increasing the total electron-beam current, the current density, and the space charge neutralization (i.e., ion density). The total beam current is likely to be limited by instabilities such as those that occur in backward-wave oscillators. The current density is likely to be limited by the brightness of future electron guns, and the (poorly understood) super-emissive, hollow-cathode discharge is a leading candidate for an electron gun. The ion density will be limited by a two-stream instability. The performance of electron-beam ion traps is also limited by discharges and instabilities involving trapped secondary electrons. These phenomena are not understood to the degree necessary to design a reliable next-generation device. Progress has been made only by trial and error. It is possible that the ion output could be enhanced by an even larger amount simply by making the trap longer, but success will again depend on understanding plasma properties of these devices. A plasma research program in this area might also spin off benefits for other electron-beam devices (e.g., klystrons, traveling-wave tubes, and free-electron lasers) and for other plasma devices (e.g., electron-cyclotron-resonance ion sources and the pure electron or pure ion plasmas described above). In addition to issues related to the electron beam itself, it is known that many electron-beam devices are affected by trapped ions. New types of devices could also evolve from the present experimental configurations of electron-beam ion traps, which, for example, might provide new and inexpensive laboratory sources of x-rays and highly charged ions and microwave devices with trapped ions designed into their operation. Radiation Sources The increased understanding of single-component plasmas is likely to have significant impact on the development of beam-type microwave devices, particularly for use in high-power and high-frequency applications. Such applications are discussed in more detail in the section on beams and radiation sources. Pressure Standard in Ultrahigh-Vacuum Regime A pure electron plasma confined in a Penning trap can potentially be used to develop a primary pressure standard in the ultrahigh-vacuum regime (<10-5Pa).
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Plasma Science: From Fundamental Research to Technological Applications The trapped electrons relax to a well-defined equilibrium state in which the average rotation frequency of the electron plasma is independent of radius. When a neutral gas is present, collisions between electrons and neutrals perturb the plasma and modify the rotation frequency and electron distribution function. By using a reference value for the elastic momentum transfer cross section of the neutrals, the neutral gas density consistent with the observed evolution of the electron plasma can be determined and used to develop a pressure standard. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS In the past two decades, much progress has been made in the understanding of nonneutral and single-component plasmas. New experimental configurations have been discovered and exploited, leading to a better understanding of the underlying physical principles of plasma confinement, approach to equilibrium, and in some cases, mechanisms of plasma transport. There are many potential scientific and technological uses of such plasmas. These opportunities result, at least in part, from the excellent confinement properties that distinguish single-component plasmas from neutral plasmas and enable true thermal equilibrium states to be achieved. Therefore, plasmas with controlled departures from equilibrium also can be created. This allows a study of nonequilibrium plasma phenomena with a degree of precision unachievable in other plasma systems. Experiments in nonneutral plasmas, such as those described above, can be exploited to address forefront problems in atomic, molecular, and optical physics and in fluid dynamics, as well as in plasma physics. Consequently, it is expected that this will continue to be a vital and productive area in plasma physics research for the foreseeable future. Since these experiments can typically be done with a relatively modest expenditure of resources, they are ideally suited to a university setting. In addition to the intrinsic scientific value of research in nonneutral plasmas, there are many important applications of these plasmas. Several examples, discussed above and in Chapter 5, "Beams, Accelerators, and Coherent Radiation Sources," include beam-type microwave devices, such as gyrotrons and free-electron lasers, precision clocks and mass spectrometers, and future generations of ion sources. The progress in this area has benefited greatly by steady support from a dedicated program at the Office of Naval Research and support from the National Science Foundation and the Department of Energy. It is the conclusion of the panel that research on nonneutral plasmas should be considered a vital part of a healthy and vigorous plasma science program in the United States in the next decade. Therefore, the panel recommends that continued strong support be given to research on nonneutral plasmas and to the development of technological applications.
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